Contents

This page is based on page C24 of the 1996 Astronomical
Almanac which provides a method for finding the position
of the Sun in the sky to an accuracy of 0.01 degree between the
years 1950 and 2050.

The formulas are based on an elliptical orbit for the Earth,
using mean orbital elements and a two term approximation for the
'equation of centre'. There is also an approximate allowance made
for the change in obliquity of the ecliptic with time, needed
when converting to right ascension and declination. The positions
are thus apparent positions, they are referred to the mean
ecliptic and equinox of date.

I compared the positions found using this low precision
formula with values referred to the mean ecliptic and equinox of
date from a more accurate program. The results (for the whole
1950 to 2050 range) are summarised below. I found the series to
be accurate within 3 seconds of RA and 15 arc seconds in
declination.

Below, I give the formulas from page C24 of the
Astronomical Almanac, with modified notation. I have
given the formulas together with numerical values for a specific
day. The calculations were done on a normal scientific calculator
with 8 figure accuracy.

I modified the QBASIC program above to produce a
file of positions for days from -20,000 to +20,000 - a 106 year
period centred on J2000.0. The RA and DEC figures were rounded to
4 places of decimals in this file. I used Planeph to generate a
similar file of positions for the Sun, referred to the mean
ecliptic and equinox of date. I then loaded both files into a
spreadsheet, and found the errors in seconds of time (RA) and
arcseconds (DEC). The maximum and minimum errors are shown in the
table below for various ranges of time about J2000.0